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<div class="title">ConditionEstimator.h</div>  </div>
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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="comment">// This file is part of Eigen, a lightweight C++ template library</span></div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="comment">// for linear algebra.</span></div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="comment">// Copyright (C) 2016 Rasmus Munk Larsen (rmlarsen@google.com)</span></div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="comment">// This Source Code Form is subject to the terms of the Mozilla</span></div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="comment">// Public License v. 2.0. If a copy of the MPL was not distributed</span></div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="comment">// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.</span></div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160; </div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;<span class="preprocessor">#ifndef EIGEN_CONDITIONESTIMATOR_H</span></div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;<span class="preprocessor">#define EIGEN_CONDITIONESTIMATOR_H</span></div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160; </div>
<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;<span class="preprocessor">#include &quot;./InternalHeaderCheck.h&quot;</span></div>
<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160; </div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;<span class="keyword">namespace </span><a class="code" href="namespaceEigen.html">Eigen</a> {</div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160; </div>
<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;<span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160; </div>
<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Vector, <span class="keyword">typename</span> RealVector, <span class="keywordtype">bool</span> IsComplex&gt;</div>
<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;<span class="keyword">struct </span>rcond_compute_sign {</div>
<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;  <span class="keyword">static</span> <span class="keyword">inline</span> <a class="code" href="group__matrixtypedefs.html#ga2623c0d4641dda067fbdb9a009ef0c91">Vector</a> run(<span class="keyword">const</span> <a class="code" href="group__matrixtypedefs.html#ga2623c0d4641dda067fbdb9a009ef0c91">Vector</a>&amp; v) {</div>
<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;    <span class="keyword">const</span> RealVector v_abs = v.cwiseAbs();</div>
<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;    <span class="keywordflow">return</span> (v_abs.array() == <span class="keyword">static_cast&lt;</span>typename Vector::RealScalar<span class="keyword">&gt;</span>(0))</div>
<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;            .select(<a class="code" href="classEigen_1_1DenseBase.html#a2755cb4023f7376880523626a8e05101">Vector::Ones</a>(v.size()), v.cwiseQuotient(v_abs));</div>
<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;  }</div>
<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;};</div>
<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160; </div>
<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;<span class="comment">// Partial specialization to avoid elementwise division for real vectors.</span></div>
<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Vector&gt;</div>
<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;<span class="keyword">struct </span>rcond_compute_sign&lt;<a class="code" href="group__matrixtypedefs.html#ga2623c0d4641dda067fbdb9a009ef0c91">Vector</a>, <a class="code" href="group__matrixtypedefs.html#ga2623c0d4641dda067fbdb9a009ef0c91">Vector</a>, false&gt; {</div>
<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;  <span class="keyword">static</span> <span class="keyword">inline</span> <a class="code" href="group__matrixtypedefs.html#ga2623c0d4641dda067fbdb9a009ef0c91">Vector</a> run(<span class="keyword">const</span> <a class="code" href="group__matrixtypedefs.html#ga2623c0d4641dda067fbdb9a009ef0c91">Vector</a>&amp; v) {</div>
<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;    <span class="keywordflow">return</span> (v.array() &lt; <span class="keyword">static_cast&lt;</span>typename Vector::RealScalar<span class="keyword">&gt;</span>(0))</div>
<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;           .select(-<a class="code" href="classEigen_1_1DenseBase.html#a2755cb4023f7376880523626a8e05101">Vector::Ones</a>(v.size()), <a class="code" href="classEigen_1_1DenseBase.html#a2755cb4023f7376880523626a8e05101">Vector::Ones</a>(v.size()));</div>
<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;  }</div>
<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;};</div>
<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160; </div>
<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Decomposition&gt;</div>
<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;<span class="keyword">typename</span> Decomposition::RealScalar rcond_invmatrix_L1_norm_estimate(<span class="keyword">const</span> Decomposition&amp; dec)</div>
<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;{</div>
<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> Decomposition::MatrixType MatrixType;</div>
<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> Decomposition::Scalar Scalar;</div>
<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> Decomposition::RealScalar RealScalar;</div>
<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> internal::plain_col_type&lt;MatrixType&gt;::type <a class="code" href="group__matrixtypedefs.html#ga2623c0d4641dda067fbdb9a009ef0c91">Vector</a>;</div>
<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> internal::plain_col_type&lt;MatrixType, RealScalar&gt;::type RealVector;</div>
<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;  <span class="keyword">const</span> <span class="keywordtype">bool</span> is_complex = (NumTraits&lt;Scalar&gt;::IsComplex != 0);</div>
<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160; </div>
<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;  eigen_assert(dec.rows() == dec.cols());</div>
<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;  <span class="keyword">const</span> <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> n = dec.rows();</div>
<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;  <span class="keywordflow">if</span> (n == 0)</div>
<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;    <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160; </div>
<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;  <span class="comment">// Disable Index to float conversion warning</span></div>
<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;<span class="preprocessor">#ifdef __INTEL_COMPILER</span></div>
<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;<span class="preprocessor">  #pragma warning push</span></div>
<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;<span class="preprocessor">  #pragma warning ( disable : 2259 )</span></div>
<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;  <a class="code" href="group__matrixtypedefs.html#ga2623c0d4641dda067fbdb9a009ef0c91">Vector</a> v = dec.solve(<a class="code" href="classEigen_1_1DenseBase.html#a2755cb4023f7376880523626a8e05101">Vector::Ones</a>(n) / Scalar(n));</div>
<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;<span class="preprocessor">#ifdef __INTEL_COMPILER</span></div>
<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;<span class="preprocessor">  #pragma warning pop</span></div>
<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160; </div>
<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;  <span class="comment">// lower_bound is a lower bound on</span></div>
<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;  <span class="comment">//   ||inv(matrix)||_1  = sup_v ||inv(matrix) v||_1 / ||v||_1</span></div>
<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;  <span class="comment">// and is the objective maximized by the (&quot;super-&quot;) gradient ascent</span></div>
<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;  <span class="comment">// algorithm below.</span></div>
<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;  RealScalar lower_bound = v.template lpNorm&lt;1&gt;();</div>
<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;  <span class="keywordflow">if</span> (n == 1)</div>
<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;    <span class="keywordflow">return</span> lower_bound;</div>
<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160; </div>
<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;  <span class="comment">// Gradient ascent algorithm follows: We know that the optimum is achieved at</span></div>
<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;  <span class="comment">// one of the simplices v = e_i, so in each iteration we follow a</span></div>
<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;  <span class="comment">// super-gradient to move towards the optimal one.</span></div>
<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;  RealScalar old_lower_bound = lower_bound;</div>
<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;  <a class="code" href="group__matrixtypedefs.html#ga2623c0d4641dda067fbdb9a009ef0c91">Vector</a> sign_vector(n);</div>
<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;  <a class="code" href="group__matrixtypedefs.html#ga2623c0d4641dda067fbdb9a009ef0c91">Vector</a> old_sign_vector;</div>
<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;  <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> v_max_abs_index = -1;</div>
<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;  <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> old_v_max_abs_index = v_max_abs_index;</div>
<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 0; k &lt; 4; ++k)</div>
<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;  {</div>
<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;    sign_vector = internal::rcond_compute_sign&lt;Vector, RealVector, is_complex&gt;::run(v);</div>
<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;    <span class="keywordflow">if</span> (k &gt; 0 &amp;&amp; !is_complex &amp;&amp; sign_vector == old_sign_vector) {</div>
<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;      <span class="comment">// Break if the solution stagnated.</span></div>
<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;      <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;    }</div>
<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;    <span class="comment">// v_max_abs_index = argmax |real( inv(matrix)^T * sign_vector )|</span></div>
<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;    v = dec.adjoint().solve(sign_vector);</div>
<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;    v.real().cwiseAbs().maxCoeff(&amp;v_max_abs_index);</div>
<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;    <span class="keywordflow">if</span> (v_max_abs_index == old_v_max_abs_index) {</div>
<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;      <span class="comment">// Break if the solution stagnated.</span></div>
<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;      <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;    }</div>
<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;    <span class="comment">// Move to the new simplex e_j, where j = v_max_abs_index.</span></div>
<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;    v = dec.solve(<a class="code" href="classEigen_1_1MatrixBase.html#ac7a03a61014f37ddd2fe61ebac0c9539">Vector::Unit</a>(n, v_max_abs_index));  <span class="comment">// v = inv(matrix) * e_j.</span></div>
<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;    lower_bound = v.template lpNorm&lt;1&gt;();</div>
<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;    <span class="keywordflow">if</span> (lower_bound &lt;= old_lower_bound) {</div>
<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;      <span class="comment">// Break if the gradient step did not increase the lower_bound.</span></div>
<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;      <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;    }</div>
<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;    <span class="keywordflow">if</span> (!is_complex) {</div>
<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;      old_sign_vector = sign_vector;</div>
<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;    }</div>
<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;    old_v_max_abs_index = v_max_abs_index;</div>
<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;    old_lower_bound = lower_bound;</div>
<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;  }</div>
<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;  <span class="comment">// The following calculates an independent estimate of ||matrix||_1 by</span></div>
<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;  <span class="comment">// multiplying matrix by a vector with entries of slowly increasing</span></div>
<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;  <span class="comment">// magnitude and alternating sign:</span></div>
<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;  <span class="comment">//   v_i = (-1)^{i} (1 + (i / (dim-1))), i = 0,...,dim-1.</span></div>
<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;  <span class="comment">// This improvement to Hager&#39;s algorithm above is due to Higham. It was</span></div>
<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;  <span class="comment">// added to make the algorithm more robust in certain corner cases where</span></div>
<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;  <span class="comment">// large elements in the matrix might otherwise escape detection due to</span></div>
<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;  <span class="comment">// exact cancellation (especially when op and op_adjoint correspond to a</span></div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;  <span class="comment">// sequence of backsubstitutions and permutations), which could cause</span></div>
<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;  <span class="comment">// Hager&#39;s algorithm to vastly underestimate ||matrix||_1.</span></div>
<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;  Scalar alternating_sign(RealScalar(1));</div>
<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;  <span class="keywordflow">for</span> (<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i = 0; i &lt; n; ++i) {</div>
<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;    <span class="comment">// The static_cast is needed when Scalar is a complex and RealScalar implements expression templates</span></div>
<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;    v[i] = alternating_sign * <span class="keyword">static_cast&lt;</span>RealScalar<span class="keyword">&gt;</span>(RealScalar(1) + (RealScalar(i) / (RealScalar(n - 1))));</div>
<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;    alternating_sign = -alternating_sign;</div>
<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;  }</div>
<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;  v = dec.solve(v);</div>
<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;  <span class="keyword">const</span> RealScalar alternate_lower_bound = (2 * v.template lpNorm&lt;1&gt;()) / (3 * RealScalar(n));</div>
<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;  <span class="keywordflow">return</span> numext::maxi(lower_bound, alternate_lower_bound);</div>
<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;}</div>
<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160; </div>
<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Decomposition&gt;</div>
<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;<span class="keyword">typename</span> Decomposition::RealScalar</div>
<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;rcond_estimate_helper(<span class="keyword">typename</span> Decomposition::RealScalar matrix_norm, <span class="keyword">const</span> Decomposition&amp; dec)</div>
<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;{</div>
<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> Decomposition::RealScalar RealScalar;</div>
<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;  eigen_assert(dec.rows() == dec.cols());</div>
<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;  <span class="keywordflow">if</span> (dec.rows() == 0)                        <span class="keywordflow">return</span> NumTraits&lt;RealScalar&gt;::infinity();</div>
<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;  <span class="keywordflow">if</span> (numext::is_exactly_zero(matrix_norm)) <span class="keywordflow">return</span> RealScalar(0);</div>
<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;  <span class="keywordflow">if</span> (dec.rows() == 1)                        <span class="keywordflow">return</span> RealScalar(1);</div>
<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;  <span class="keyword">const</span> RealScalar inverse_matrix_norm = rcond_invmatrix_L1_norm_estimate(dec);</div>
<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;  <span class="keywordflow">return</span> (numext::is_exactly_zero(inverse_matrix_norm) ? RealScalar(0)</div>
<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;                                                       : (RealScalar(1) / inverse_matrix_norm) / matrix_norm);</div>
<div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;}</div>
<div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160; </div>
<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;}  <span class="comment">// namespace internal</span></div>
<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160; </div>
<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;}  <span class="comment">// namespace Eigen</span></div>
<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160; </div>
<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="ttc" id="aclassEigen_1_1DenseBase_html_a2755cb4023f7376880523626a8e05101"><div class="ttname"><a href="classEigen_1_1DenseBase.html#a2755cb4023f7376880523626a8e05101">Eigen::DenseBase::Ones</a></div><div class="ttdeci">static const ConstantReturnType Ones()</div><div class="ttdef"><b>Definition:</b> CwiseNullaryOp.h:672</div></div>
<div class="ttc" id="aclassEigen_1_1MatrixBase_html_ac7a03a61014f37ddd2fe61ebac0c9539"><div class="ttname"><a href="classEigen_1_1MatrixBase.html#ac7a03a61014f37ddd2fe61ebac0c9539">Eigen::MatrixBase::Unit</a></div><div class="ttdeci">static const BasisReturnType Unit(Index size, Index i)</div><div class="ttdef"><b>Definition:</b> CwiseNullaryOp.h:904</div></div>
<div class="ttc" id="agroup__matrixtypedefs_html_ga2623c0d4641dda067fbdb9a009ef0c91"><div class="ttname"><a href="group__matrixtypedefs.html#ga2623c0d4641dda067fbdb9a009ef0c91">Eigen::Vector</a></div><div class="ttdeci">Matrix&lt; Type, Size, 1 &gt; Vector</div><div class="ttdoc">[c++11] Size×1 vector of type Type.</div><div class="ttdef"><b>Definition:</b> Matrix.h:544</div></div>
<div class="ttc" id="anamespaceEigen_html"><div class="ttname"><a href="namespaceEigen.html">Eigen</a></div><div class="ttdoc">Namespace containing all symbols from the Eigen library.</div><div class="ttdef"><b>Definition:</b> Core:139</div></div>
<div class="ttc" id="anamespaceEigen_html_a62e77e0933482dafde8fe197d9a2cfde"><div class="ttname"><a href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Eigen::Index</a></div><div class="ttdeci">EIGEN_DEFAULT_DENSE_INDEX_TYPE Index</div><div class="ttdoc">The Index type as used for the API.</div><div class="ttdef"><b>Definition:</b> Meta.h:59</div></div>
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